Solve 3(x-2)+5<4(x-1)+6

$$3 ( x - 2 ) + 5 < 4 ( x - 1 ) + 6$$

Solve for x

$$x>-3$$

Solution Steps

Use the distributive property to multiply 3 by x-2.

$$3x-6+5<4\left(x-1\right)+6$$

Add -6 and 5 to get -1.

$$3x-1<4\left(x-1\right)+6$$

Use the distributive property to multiply 4 by x-1.

$$3x-1<4x-4+6$$

Add -4 and 6 to get 2.

$$3x-1<4x+2$$

Subtract 4x from both sides.

$$3x-1-4x<2$$

Combine 3x and -4x to get -x.

$$-x-1<2$$

Add 1 to both sides.

$$-x<2+1$$

Add 2 and 1 to get 3.

$$-x<3$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x>-3$$